I inherited these plants (what are they ?) and they were in pots that even I could see were far too small. They are much happier since I repotted them but this one has a bad case of the droops. So should I cut it back or just leave it ? If the answer is "cut" , how far back? Grateful for any constructive suggestions since I have no idea what I am doing

I think it's Frangipani? Try looking it up on Google.

Google " Desert Rose" that is what it is. The plant is a bit leggy and could do with a trim.

Looks like that one had its root ball overly disturbed. Like its relative the frangipani, new branches will grow from the location of the cuts. I suggest starting with the two branches that have further branches, snipping them just after the first split. A few months later, cut back the one spindly branch on the right. In this way, you will have narrowed the plant's shape without depriving it of all its leaves. 

 

Note that this advice assumes that the pot has adequate drainage. If there wasn't a pot shard or big gravel over the hole in the bottom, the plant might just be drowning. 

Thanks to all for the suggestions and advice. I wanted to cut it back and now I have some idea how to go about it.